ENGLISH IN STATISTICS AND COMBINATORICS Kelompok 4
ENGLISH IN STATISTICS AND COMBINATORICS Kelompok 4
ENGLISH IN STATISTICS AND COMBINATORICS Kelompok 4
IN 1
3x + 2 x STATISTICS
AND
COMBINAT
GROUP 4
• ANGGUN FILISIA ACUNA (4101422052)
CONTINGENCY TABLE
BAR CHART
Even Data
Median group data
Where,
lower limit of median class
cumulative frequency of the class preceding the median class
total number of observations
frequency of the median class
class size
Mo
de
The mode is the value that appears most frequently in a data set.
Mode of Ungroup data
For Ungroup data, we just need to identify the observation which occurs maximum
times.
Mode of Group data
Quartile
A quartile is a value that divides the data into 4 parts with
the same size or size that divides the data into 4 equal
parts.
Where ,
: Many / amount of data
: bottom edge
: class length
: frequency Q1
: cumulative frequency before Q1
: quartile to-i
: data value to -i
• INTERQUARTILE RANGE
The “Interquartile Range” is from Q1 to Q3.
To calculate it just subtract Quartile 1 from Quartile 3.
Percenti
le
The values dividing the data into 100 equal parts.
In the method of determining percentiles, it is divided into 2 types of methods, including the following:
Single data percentile
Where ,
: Many / amount of data
: bottom edge
: class length
: frequency P1
: cumulative frequency before P1
: persentile to-i
: data value to -i
Desil
The values that divide the data into 10 equal parts.
In the method of determining deciles, it is divided into 2 types of methods, including the following:
Single data decile
Group data decile
Where,
: Many / amount of data
: bottom edge
: class length
: frequency D1
: cumulative frequency before D1
: desik to-i
: data value to -i
RANGE
Where ,
: frequency
: amount of data
: the mean
STANDARD DEVIATION
The standard deviation is the square root of the variance and indicates the standard deviation
of the data from the mean. The usual standard deviation is symbolized by atau .
b. Standard deviation for group data
Where,
: frequency
: amount of data
: the mean
MEAN deviation
The mean deviation is the absolute value of the difference between each value ()
and the mean value () divided by the number of data (n).
In Mathematics it is denoted as the abbreviation SR or MD.
Single Data Mean Deviation Formula
In single data, we can calculate it by dividing the difference between the data
values and the mean value of the data values:
Where,
SR = Mean Deviation
= data value to -i
= the mean value of grouped data
n = a lot of data
MEAN deviation
Group Data Mean Deviation Formula
In group data it can be calculated by dividing the total of multiplying the
difference between the mean and the median value by the frequency of the
total number of all data frequencies as follows:
Where,
SR = Mean Deviation
= the frequency of the i-class data
= the middle value of the i-class data
̄ = the mean value of grouped data
W H AT IS QUESTIO
N ATO R I C ? N #2
CO M B I
Formula
Where –
• represents factorial
• number of sets
Example
Calculate the factorial of 5 i.e. 5!.
Solution:
Multiply all the whole numbers up to the number considered.
PERMUTATION
A permutation is an arrangement of all or part of a set of
objects, with regard to the order of the arrangement.
Where –
• number of the set form which elements are permuted.
• size of each permutation.
• are non negative integers.
PERMUTATION WITH
REPLACEMENT
Permutation with replacement is defined and given by the
following function:
Where –
• number of items which can be selected.
• number of items which are selected.
• ordered list of items or permutations.
PERMUTATION WITH
REPLACEMENT
Example: Electronic device usually require a personal code to
operate. This particular device uses 4-digit. Calculate how many
codes are possible.
Solution:
Each code is represented by r=4 permutation with replacement
of set of 10 digits {0,1,2,3,4,5,6,7,8,9}
CIRCULAR PERMUTATION
Circular permutation is the total number of ways in which n distinct
bjects can be arranged around a fix circle. It is two types.
• Case 1 – Clockwise and Anticlockwise orders are different.
Where –
• represents circular permutation
• number of objects
COMBINATION
A combination is an arrangement of elements whose order does not
matter.